Southwestern University Case Study B

Anthony Lawrence

Problem: Southwestern University is experiencing a quickly expanding football program. As a result, attendance for home games is increasing and approaching capacity. It is in the best interest of SWU to forecast attendance to aid them in deciding when the best time to expand the present stadium, which now holds 54,000.

Data: The following data is from the past six seasons, 2002-2007.

Game Attendance Year – Game – Opponent 2002-1 Baylor 34200 2002-2 Texas 39800 2002-3 LSU 38200 2002-4 Arkansas 26900 2002-5 USC 35100 2003-1 Oklahoma 36100 2003-2 Nebraska 40200 2003-3 UCLA 39100 2003-4 Nevada 25300 2003-5 Ohio State 36200 2004-1 TCU 35900 2004-2 Texas Tech 46500 2004-3 Alaska 43100 2004-4 Arizona 27900 2004-5 Rice 39200 2005-1 Arkansas 41900 2005-2 Missouri 46100 2005-3 Florida 43900 2005-4 Miami 30100 2005-5 Duke 40500 2006-1 Indiana 42500 2006-2 North Texas 48200 2006-3 Texas A&M 44200 2006-4 Southern 33900 2006-5 Oklahoma 47800 2007-1 LSU 46900 2007-2 Texas 50100 2007-3 Prairie View A&M 45900 2007-4 Montana 36300 2007-5 Arizona State 49900 An important thing to note is that the homecoming game of every season is the second home game (bold), and is always well attended. Also the forth home game always corresponds with a local festival that always draws from attendance (italics). Anthony Lawrence

Summary of Forecasting Methods: Below is a table of the forecasting methods. The correlation coefficient, bias, mean absolute deviation (MAD), mean squared error (MSE), and mean absolute percent error (MAPE) are shown.

Correlation Bias MAD MSE MAPE Naïve -- 541.38 6865.52 69,856,200 .19

Moving Average -- 491.36 6,138.27 59,540,560 .17 (3 periods) Weighted Moving Average -- 424.81 6,501.58 61,107,180 .18 (3 period; .6, .3, .1) Exponential smoothing -- 794.28 5,880.56 50,755,960 .16 (alpha = 0.5) Trend Analysis .54 0.00 4,355.70 31,285,700 .12

Seasonal Additive .97 0.00 1,251.26 2,386,650 .03 Decomposition

It is obvious that the superior method is seasonal additive decomposition. This makes sense because of the cyclical nature each season follows, largely due to the homecoming game and local festival. The other methods cannot take those variations into account, and this adversely affects their error. Because of this they are not suitable for predicting at which point the demand of attendance will surpass the stadium’s capacity. They will show when the average or smoothed demand will reach capacity, but this will occur after attendance for one or two games will consistently surpass capacity. Seasonal additive decomposition is definitely the best method, and all indications support that. The bias for trend analysis is just the same as seasonal, however the correlation coefficient is not acceptable for this method, well below .70, but the seasonal correlation is outstanding at .97. So, now the management has a decision to make whether or not it is worth putting off expansion of the stadium until the average attendance of a season is above capacity, and losing potential ticket sales for the games that are above capacity, or to go ahead and expand before capacity is ever reached in a single game. Anthony Lawrence

Forecasting: The following table shows the forecasted attendance of the next two seasons of home games.

Game Attendance 2008 – 1 46540.23 2008 – 2 52555.73 2008 – 3 50254.56 2008 – 4 38370.06 2008 – 5 50202.22 2009 – 1 48784.39 2009 – 2 54799.89 2009 – 3 52498.72 2009 – 4 40614.22 2009 – 5 52446.38

According to this analysis, the second game of 2009, the homecoming game, will be the first game that the demand for attendance will exceed capacity. The management can wait until after the 2008 season to start the completion, so long as it is completed before the 2009 season starts. One thing they should consider is that a refurbished stadium would cause a spike in attendance because fans would want to see and experience the new facilities. With this in mind, these figures could be much lower than what would actually happen if an expansion were built.

Revenues: Ticket sales will average $20 in 2008 and $21 in 2009 due to a 5% price increase. Total sales can be found for each season by summing the attendance from each game and multiplying by the ticket price. The results are displayed in the table below.

Season Total Attendance Revenue 2008 237,922.8 $4,758,456 2009 249,143.6 $5,232,016

Again, it should be emphasized that depending on when the expansion is built, these values could be lower than what actually comes in. It would be smart for them to build the expansion sooner than later, so that the spike in ticket sales will come sooner. This could offset some extra costs that could incur from building it sooner.